Coupled meshfree (SPH) and grid based (FDM) procedures for modeling fluid flow through deformable porous media

Abstract

A coupled numerical framework based on smoothed particle hydrodynamics (SPH) and finite difference method (FDM) has been developed to analyze the coupled process of fluid flow in a deformable poro-elastic medium. The salient feature of the developed coupled model is that the porous media has been simulated by two separate layers to describe solid and fluid phase with their respective governing equations and solved simultaneously with mutual transfer of variables from one phase to another. SPH being meshfree method has advantage over grid based methods to simulate large deformations and fracture propagation and hence used for simulating the solid phase while the pore pressure variation in the fluid phase has been analyzed by FDM. Detailed mathematical framework and procedure explaining the mutual exchange of information between SPH and FDM has been discussed in this paper. The change of porosity due to solid deformation and its impact on variation of fluid pressure has also been included in the proposed model. The developed coupled model has been finally validated with three standard benchmark problems by comparing numerical results of the proposed model with those of analytical solutions, to establish its accuracy and versatility in modeling fluid flow through deformable porous rock media.